Question: Solve for $n$, $ -\dfrac{6}{3n} = -\dfrac{9}{12n} - \dfrac{4n - 3}{9n} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3n$ $12n$ and $9n$ The common denominator is $36n$ To get $36n$ in the denominator of the first term, multiply it by $\frac{12}{12}$ $ -\dfrac{6}{3n} \times \dfrac{12}{12} = -\dfrac{72}{36n} $ To get $36n$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{9}{12n} \times \dfrac{3}{3} = -\dfrac{27}{36n} $ To get $36n$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{4n - 3}{9n} \times \dfrac{4}{4} = -\dfrac{16n - 12}{36n} $ This give us: $ -\dfrac{72}{36n} = -\dfrac{27}{36n} - \dfrac{16n - 12}{36n} $ If we multiply both sides of the equation by $36n$ , we get: $ -72 = -27 - 16n + 12$ $ -72 = -16n - 15$ $ -57 = -16n $ $ n = \dfrac{57}{16}$